摘要
设D为R^d(d≥3)中非空规则开子集.本文利用超布朗运动给出了一类非线性方程Dirichlet问题非负有界解的通式.在一定条件下证明了满足在无穷远处有规定极限非负有界解的存在唯一性,并给出了解的概率表达式,推广了Dynkin中的结果.
Suppose D is a nonempty regular open set in Rd (d≥ 3). This paper gives the usual formula of the nonegative bounded solution for the Dirichlet problem for one class of nonlinear equations by using super Brownian motion. Under some conditions, this paper proves the existence and the uniqueness for the Dirichlet problem have fixed limit at infinity and obtain the probabilistic formula and extended some results in [4].
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1997年第1期37-42,共6页
Acta Mathematica Sinica：Chinese Series
基金
河南省自然科学基金
国家自然科学基金
天元基金
